The above theorem, its extensions, and the methods of their proofs, have had a host of applications. Among many other applications, they are used by Yang [1]} to verify the Katz–Sarnak heuristics [2]} for low-lying zeroes of Dedekind zeta
functions of cubic fields; by
Bhargava–Wood [3]}, Belabas–Fouvry [4]} and Wang [5]} to prove Malle's conjecture for various different Galois
groups; by Martin–Pollack [6]} and Cho–Kim [7]} to obtain
the average value of the smallest prime satisfying certain prescribed
splitting conditions.
